Abstract
We consider the degree/diameter problem for directed planar graphs. We show that planar digraphs with diameter 2 and maximum out-degree and in-degree d, d ≥ 41, cannot have more than 2d vertices. We show that 2d is the best possible upper bound by constructing planar digraphs of diameter 2 having exactly 2d vertices.
Furthermore, we give upper and lower bounds for the largest possible order of planar digraphs with diameter greater than 2.
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Simanjuntak, R., Miller, M. (2005). Maximum Order of Planar Digraphs. In: Akiyama, J., Baskoro, E.T., Kano, M. (eds) Combinatorial Geometry and Graph Theory. IJCCGGT 2003. Lecture Notes in Computer Science, vol 3330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30540-8_18
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DOI: https://doi.org/10.1007/978-3-540-30540-8_18
Publisher Name: Springer, Berlin, Heidelberg
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